A positive integer satisfies the ratio ^ n C_ 3 : ^ n C_ 2 = 4 : 1

MATHEMATICS · Multi-part · CBSE · Mathematics · Permutations and Combinations · Permutations and Combinations

Problem

A positive integer

n

satisfies the ratio

{}^{n}C_{3} : {}^{n}C_{2} = 4 : 1.

Answer the following questions. (i) Translate the given ratio into an algebraic equation in

n

. (ii) Solve the equation to find the value of

n

. (iii) Confirm that the obtained value of

n

indeed yields the stated ratio of

4:1